Question

In the given figure, $\angle PQR=\angle PRQ$, then prove that $\angle PQS=\angle PRT.$

Answer 1

In the given figure, $ST$ is a straight line and ray $QP$ stands on it.
$\therefore \angle PQS+\angle PQR={180}^{\circ }$ ( Linear Pair)
$\angle PQR={180}^{\circ }-\angle PQS$……………..(1)
$\angle PRT+\angle PRQ={180}^{\circ }$ (Linear pair)
$\angle PRQ={180}^{\circ }-\angle PRT$……………(2)
It is given that $\angle PQR=\angle PRQ.$
Equating equation (1) and (2), we obtain,
${180}^{\circ }-\angle PQS={180}^{\circ }-\angle PRT$
$\angle PQS=\angle PRT$

Hence proved.